In terms of raw magical power then folks like Xerath (when he's out of his sarcophagus), Bard and Kindred are pretty much the strongest.
In terms of raw physical power Malphite comes out on top because he has all the physical prowess of a sodding mountain. I don't care how many champions have done earth shattering feats, Malphite could do all of this with substantially less effort, and then some.
The weakest in terms of magical power are the champions who have no magic on them in any way, so basically the more average humans. Even yordles rank higher than the average human in this example because as we've recently learned, all yordles have magic, as it is innate for them. Humans are very rarely born with innate magic and have to learn it.
In terms of physical weakness Corki, Heimerdinger, Annie, Amumu, Zilean and Twitch would be in this area, because they're either sunstantially older than other champions and that age works against them biologically, are too young and thus can't physically defend themselves well, or have the physical capabilities of a ridiculously large but still smaller than the average human rat. I'm sorry Twitch but seriously, you wouldn't win in a fight with...anyone else in the League roster in a test of strength. I mean that's why Twitch's playstyle and way of life revolves around being an ambush predator.